7 ms·

This was a great read! But I wish the article would have mentioned how tiny the microscopic time-reversal effects are, compared to macroscopic time reversal. Th

by maho 11y ago

This was a great read! But I wish the article would have mentioned how tiny the microscopic time-reversal effects are, compared to macroscopic time reversal. The microscopic effects are too small to explain why we have such a clear direction of time. Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible. In fact, you can build a toy-universe in your head, where all interactions are time-reversible, and you would still observe that the chaotic-ness increases with time, unless you start with a completely random initial state (in which the chaoticness stays roughly constant). This increase in chaoticness is comletely unsurprising: It's a simple consequence of the fact that there are much, much more "states" in which a system looks chaotic, than states in which it looks ordered. Therefore, a system transitioning from state to state is much more likely to be in one that looks chaotic, and very, very unlikely to ever go back to a state that is non-chaotic. The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Why did the universe not start out in a state that is essentially equal to the heat-death [1]? The microscopic processes that are not time-reversible might have something to do with this, but it's not clear at all how they can solve this mystery. [1] https://en.wikipedia.org/wiki/Heat_death_of_the_universe https://en.wikipedia.org/wiki/Heat_death_of_the_universe

blaze33 11y ago
As I understand it, the universe actually started in a heat-death state (very small temperature differences, homogeneous and isotropic), it's just that it is a very hot heat death state, not the usual cold one where everything freezes. Then it is the universe expansion that made the entropy per volume decrease, actually allowing complex systems to evolve. The expansion still has to occur faster than the entropy increase rate but I read somewhere that the universe total entropy did not increase that much since the Big Bang.
- charlieflowers 11y ago
  Or whole universe was in a hot dense state. Then, nearly 14 million years ago, expansion started. Wait ... The earth began to cool.
  - tyho 11y ago
    *billion
    - charlieflowers 11y ago
      Oh crap, that typo makes me sound like a Young Earth crackpot :)
roberto 11y ago
> Therefore, a system transitioning from state to state is much more likely to be in one that looks chaotic, and very, very unlikely to ever go back to a state that is non-chaotic. This one thing I don't understand about the 2nd law of thermodynamics: given enough time won't the system go back to a more organized state simply by chance? And in that case, wouldn't the total entropy be reduced?
- TTPrograms 11y ago
  Yes, that can happen, but with overwhelmingly small probability. Say if you consider the probability that all the gas atoms in a box spontaneously are in one half of the box, the chance is approximately (1/2)^N, where N is on the order of Avogadro's number.
- nabla9 11y ago
  You understand it just fine. What may be nonintuitive is the incredibly low change of that happening even in microscopic scale. Difference between macroscopic 'organized states' vs 'unorganized states' just mind mindbogglingly huge.
- TeMPOraL 11y ago
  As others said, your understanding is fine - you just need to gain the appreciation to how much more unordered states are there for a system to be in than the ordered ones. My physics professor used to underscore it by drawing diagrams that show a line that suddenly goes from almost 0 to "the tip of this line is somewhere in the next galaxy". Or to give you a somewhat similar problem - consider a 32x32px 8bit image (a standard Windows icon since version 3.0). The image consists of 1024 pixels, each capable of representing a different color from the set of 256 colors. How many possible pictures like this are there? Or, as you'd ask in thermodynamics, in how many states such a system can be? It's 256 states per pixel raised to 1024th power (just like 6-digit binary number has 2^6 possible values). It's 256^1024. You know how much is it? 10907481356194159294629842447337828624482641619962326924318327861897213318491192 95216264234525201987223957291796157025273109870820177184063610979765077554799078 90629884219298953860982522804820515969685161359163819677188654260932456012129055 39018863010179002525357999172000100796000265358368009052978058809523505016301954 75653911005312364560014847426035293551245843928918752768696279344088055617515694 34994540667782514081490061610592025643850457801332649356583604724240738244281224 51315177575191648992263657437224322773680750276278830452065017927617009456991684 97257879683851737049996900961120515655050115561271491492515342105748966629547032 78632150573082843022166497032439613863525162640951616800542762343599630892169144 61811874063953106654048857394348328774281674074953709935118687563599703901170218 23616749458620969857006263612082706715408157066575137281027022310927564910276759 16052087830463241104936456875492096732298245918476342738379027244843801852697776 49410727156115804346908274593399919614142427414105991174260605564837637563145276 11362658628383368621157993638020878537675545336789915694234433955666315070087213 53547025567031200413072549583450835743965382893607708097855057891296790735278005 49356215610907958451729541159729274798775277385600082041185589300047777487277618 53813510493840581861598652211605960308356405941821189714037868726219481498727603 65361629885617482241303348543878532402475141941718301228107820972930353737280457 43720952287036227763639452908698062584223551485075710396193874496298668081887696 62815778153079393179093143648340761738581819563002994422790754955061288818308430 07964869323217915876591803556521615711540299212027615560787310793747746684152836 29877086994501520312318625942030856938389446570613462367042340268211029589549511 97087076546186622796294536451620756509351018906023773821539532776208676978589731 96633030889330466516943618507835064156833694453005143749131129883436726523859540 49042734559287239495252271846174043678547546104743770197680255766058810380772707 07717942221977090385438585844095492116099852538903974655703943973086090930596963 36076752996493841459818570596375456149735582781362383328890630900428801732142480 86639626713335280092327583508730596141187237814221014601986157473868550968960891 89180441339558524822867541113212638793675567650340362970031930023397828465318547 23824423202801518968966041882297600081543761065225427016359565087543385114712321 4227266605403581781469090806576468950587661997186505665475715792896 This much. (Source: [0]). Now ask yourself, how many of those pictures represent a letter "A". Quite a lot probably, but nowhere near that much. In all those 256^1024 pictures, you have every possible representable letter A, as well as any other possible Unicode character. In those images are all your most cherished private photos (or at least their thumbnails), and also the photos of all things that you'd wish happened but didn't. A thumbnail of every possible photo of the universe is there as well. There's also something else. Something much more frequent than all other image I've just mentioned taken together. It's the noise. The things we don't recognize, the things we consider uninteresting. I ask you, use your intuition - if you were to create a random Windows icon every second, how soon would you expect to get one depicting a letter "A"? And now realize we were talking about silly icons that are probably barely visible on your screen. There are 6.02 x 10²³ atoms in 12 grams of carbon. I.e. in a tip of your pencil. 602000000000000000000000 atoms. Those are your pixels. And if you want to compute the number of states this pile of atoms can be in, that is the number that goes in your exponent. The base is some combination of possible positions, orientations and velocities, and then probably something else I'm forgetting right now. And almost all of those states are noise. That's how the Second Rule works. [0] - http://www.wolframalpha.com/input/?i=256%5E1024 http://www.wolframalpha.com/input/?i=256%5E1024
darkmighty 11y ago
Those questions are very old. You may think the anthropic principle is sufficient here: complex systems seem to rely on an entropy gradient (no life exists in an uniformly chaotic or static state). Ludwig Boltzmann made this argument in the 19th century [1]. However, the argument can apparently be extended to the conclusion that, in a probabilistic sense, your consciousness is just a sliver of a random fluctuation of a near-maximal entropy state. Feynman argued[2] that this shows we do not arise from a random fluctuation, because (even though we're conscious), when we look far away the universe looks highly organized. Note that those arguments make a bunch of assumptions that may not be valid in our universe, and may not make cosmological sense (entropy is not well defined cosmologically). [1] https://en.wikipedia.org/wiki/Boltzmann_brain https://en.wikipedia.org/wiki/Boltzmann_brain [2] http://blogs.discovermagazine.com/cosmicvariance/2008/12/29/richard-feynman-on-boltzmann-brains/ http://blogs.discovermagazine.com/cosmicvariance/2008/12/29/...
- d4rkph1b3r 11y ago
  >Feynman argued[2] that this shows we do not arise from a random fluctuation, because (even though we're conscious), when we look far away the universe looks highly organized. Oh that is an interesting and compelling argument I have not heard! Thank you for sharing.
  - effie 11y ago
    Both Boltzmann's idea of fluctuation and Feynman's argument against it are unfortunately devoid of meaning, because we do not know how highly organized and thermal death universe look like. We never saw and probably never will see another state of the universe and there is no way to experiment with it.
    - d4rkph1b3r 11y ago
      His argument is sound. If there is infinite #s of universes, or the universe keeps reforming infinitely (implication being it will have varying degrees of uniformity), then it's mathematically probable that we would be boltzman brain's in a less coherent universe. We don't observe that.
ylem 11y ago
For those interested in the anthropomorphic principle, this paper by Wald might be interesting: http://arxiv.org/pdf/gr-qc/0507094v1.pdf http://arxiv.org/pdf/gr-qc/0507094v1.pdf
trhway 11y ago
>The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Why did the universe not start out in a state that is essentially equal to the heat-death [1]? taken as a closed system, our Universe's initial state was a heat-death and it would stay here, nothing would happen. Fortunately or unfortunately our Universe is embedded into previous very old and cool Universe, and this gradient is what drives the expansion of our Universe and thus provides for all the things we see happening to happen, including life (which is just entropy maximizing process in some conditions). 100-200+B year later our Universe will too be very cool and expanded very "thin". The matter will be collected into several hyper-super-black holes with Schwarzschild radii of tens or even hundreds o billions of light years - some probably bigger than our visible Universe (which has 10B light years Schwartzild radius). The matter inside a regular black hole is neutrons being driven into higher and higher states as result of mass being added into the black hole. At some point the neutrons get to split into gluons/quarks and those would continue to be driven into more energetic states as more mass is added, and may be split as a result into something else too. At the same time the space around becomes "thinner" and cooler. At some point, when even more mass is added, and thus this "soup" becomes even more energetic, beyond currently known physics unfortunately, something happens to the gravitational force what has been keeping it together and it explodes and start expanding (as there is extremely high gradient between the "soup" and the space of the old Universe - thus that will be a birth of new Universe inside our old Universe, inside the parent Universe of our Universe ... ad infinitum ... with non-zero gradient, though smaller and smaller as parent-child Universe pair is getting older...
effie 11y ago
> Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible. Entropy does not always increase in time, because entropy is rarely a function of time. The most common meaning of the word is a thermodynamic quantity that is not, in general, defined in non-equilibrium states. It is a function of state variables rather than time. What people are talking about when they say "entropy increases in time" is actually some variant of minus Boltzmann H-function. This kind of resembles thermodynamic entropy, but is a distinct and less general concept. There are processes where entropy gets higher but "entropy" (minus Boltzmann H-function) get lower. If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. It is not even clear how to define entropy of the system in between, since it is in highly non-equilibrium state.
- trhway 11y ago
  >If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. Moving an object to higher gravitational potential decreases the entropy of the system (and thus requires work, unsurprisingly). Mixing oil into water means you displace some volume of water which were closer to Earth with oil bubbles (which are lighter than equivalent volume of water) while you force the displaced water volume higher/further from Earth. Thus by mixing lighter oil with heavier water you decrease the entropy of the gravitational system consisting of the oil, water and Earth. Left to its own devices, the system evolves along the entropy increasing gradient - heavy water goes down displacing lighter oil up, thus decreasing the gravitational potential of the system (the friction during that "unmixing" is the work of the gravitational force that ultimately results in the heat that is lost away into the environment).
  - effie 11y ago
    When the fluids are mixed by a spoon, surely work has been done by the stirring spoon on the system and energy of the system increased. But this does not by itself imply entropy of the system increased. The reason is the system got to a non-equilibrium state which has no macroscopic thermodynamic description and no unique way to assign entropy and detect its changes.
e12e 11y ago
>Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible. Perhaps in zero-g, under the effect of no acceleration and/or gravity. But I've seen all (most of) the non-water bits settle in the bottom of a bottle left alone for a long time. That doesn't detract from your overall point about entropy, but it's probably to use an example based on the quality of energy (try to generate electricity from the heat that leeches from the walls of your cabin in winter).
bcbrown 11y ago
> The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Here's a possibility: if you "start" at a random state, after enough exploration of the state space, there would be a local minima that was arbitrarily well-ordered. Both directions of time would then view that as the "past", and the other direction as "future". These perceptions as to the arrow of time would last until a state equivalent to heat death is reached, at which point the "arrow" of time would flip around again.

by maho 11y ago

blaze33 11y ago

As I understand it, the universe actually started in a heat-death state (very small temperature differences, homogeneous and isotropic), it's just that it is a very hot heat death state, not the usual cold one where everything freezes. Then it is the universe expansion that made the entropy per volume decrease, actually allowing complex systems to evolve. The expansion still has to occur faster than the entropy increase rate but I read somewhere that the universe total entropy did not increase that much since the Big Bang.

charlieflowers 11y ago
Or whole universe was in a hot dense state. Then, nearly 14 million years ago, expansion started. Wait ... The earth began to cool.
- tyho 11y ago
  *billion
  - charlieflowers 11y ago
    Oh crap, that typo makes me sound like a Young Earth crackpot :)

roberto 11y ago

> Therefore, a system transitioning from state to state is much more likely to be in one that looks chaotic, and very, very unlikely to ever go back to a state that is non-chaotic. This one thing I don't understand about the 2nd law of thermodynamics: given enough time won't the system go back to a more organized state simply by chance? And in that case, wouldn't the total entropy be reduced?

TTPrograms 11y ago
Yes, that can happen, but with overwhelmingly small probability. Say if you consider the probability that all the gas atoms in a box spontaneously are in one half of the box, the chance is approximately (1/2)^N, where N is on the order of Avogadro's number.
nabla9 11y ago
You understand it just fine. What may be nonintuitive is the incredibly low change of that happening even in microscopic scale. Difference between macroscopic 'organized states' vs 'unorganized states' just mind mindbogglingly huge.
TeMPOraL 11y ago
As others said, your understanding is fine - you just need to gain the appreciation to how much more unordered states are there for a system to be in than the ordered ones. My physics professor used to underscore it by drawing diagrams that show a line that suddenly goes from almost 0 to "the tip of this line is somewhere in the next galaxy". Or to give you a somewhat similar problem - consider a 32x32px 8bit image (a standard Windows icon since version 3.0). The image consists of 1024 pixels, each capable of representing a different color from the set of 256 colors. How many possible pictures like this are there? Or, as you'd ask in thermodynamics, in how many states such a system can be? It's 256 states per pixel raised to 1024th power (just like 6-digit binary number has 2^6 possible values). It's 256^1024. You know how much is it? 10907481356194159294629842447337828624482641619962326924318327861897213318491192 95216264234525201987223957291796157025273109870820177184063610979765077554799078 90629884219298953860982522804820515969685161359163819677188654260932456012129055 39018863010179002525357999172000100796000265358368009052978058809523505016301954 75653911005312364560014847426035293551245843928918752768696279344088055617515694 34994540667782514081490061610592025643850457801332649356583604724240738244281224 51315177575191648992263657437224322773680750276278830452065017927617009456991684 97257879683851737049996900961120515655050115561271491492515342105748966629547032 78632150573082843022166497032439613863525162640951616800542762343599630892169144 61811874063953106654048857394348328774281674074953709935118687563599703901170218 23616749458620969857006263612082706715408157066575137281027022310927564910276759 16052087830463241104936456875492096732298245918476342738379027244843801852697776 49410727156115804346908274593399919614142427414105991174260605564837637563145276 11362658628383368621157993638020878537675545336789915694234433955666315070087213 53547025567031200413072549583450835743965382893607708097855057891296790735278005 49356215610907958451729541159729274798775277385600082041185589300047777487277618 53813510493840581861598652211605960308356405941821189714037868726219481498727603 65361629885617482241303348543878532402475141941718301228107820972930353737280457 43720952287036227763639452908698062584223551485075710396193874496298668081887696 62815778153079393179093143648340761738581819563002994422790754955061288818308430 07964869323217915876591803556521615711540299212027615560787310793747746684152836 29877086994501520312318625942030856938389446570613462367042340268211029589549511 97087076546186622796294536451620756509351018906023773821539532776208676978589731 96633030889330466516943618507835064156833694453005143749131129883436726523859540 49042734559287239495252271846174043678547546104743770197680255766058810380772707 07717942221977090385438585844095492116099852538903974655703943973086090930596963 36076752996493841459818570596375456149735582781362383328890630900428801732142480 86639626713335280092327583508730596141187237814221014601986157473868550968960891 89180441339558524822867541113212638793675567650340362970031930023397828465318547 23824423202801518968966041882297600081543761065225427016359565087543385114712321 4227266605403581781469090806576468950587661997186505665475715792896 This much. (Source: [0]). Now ask yourself, how many of those pictures represent a letter "A". Quite a lot probably, but nowhere near that much. In all those 256^1024 pictures, you have every possible representable letter A, as well as any other possible Unicode character. In those images are all your most cherished private photos (or at least their thumbnails), and also the photos of all things that you'd wish happened but didn't. A thumbnail of every possible photo of the universe is there as well. There's also something else. Something much more frequent than all other image I've just mentioned taken together. It's the noise. The things we don't recognize, the things we consider uninteresting. I ask you, use your intuition - if you were to create a random Windows icon every second, how soon would you expect to get one depicting a letter "A"? And now realize we were talking about silly icons that are probably barely visible on your screen. There are 6.02 x 10²³ atoms in 12 grams of carbon. I.e. in a tip of your pencil. 602000000000000000000000 atoms. Those are your pixels. And if you want to compute the number of states this pile of atoms can be in, that is the number that goes in your exponent. The base is some combination of possible positions, orientations and velocities, and then probably something else I'm forgetting right now. And almost all of those states are noise. That's how the Second Rule works. [0] - http://www.wolframalpha.com/input/?i=256%5E1024 http://www.wolframalpha.com/input/?i=256%5E1024

darkmighty 11y ago

Those questions are very old. You may think the anthropic principle is sufficient here: complex systems seem to rely on an entropy gradient (no life exists in an uniformly chaotic or static state). Ludwig Boltzmann made this argument in the 19th century [1]. However, the argument can apparently be extended to the conclusion that, in a probabilistic sense, your consciousness is just a sliver of a random fluctuation of a near-maximal entropy state. Feynman argued[2] that this shows we do not arise from a random fluctuation, because (even though we're conscious), when we look far away the universe looks highly organized. Note that those arguments make a bunch of assumptions that may not be valid in our universe, and may not make cosmological sense (entropy is not well defined cosmologically). [1] https://en.wikipedia.org/wiki/Boltzmann_brain https://en.wikipedia.org/wiki/Boltzmann_brain [2] http://blogs.discovermagazine.com/cosmicvariance/2008/12/29/richard-feynman-on-boltzmann-brains/ http://blogs.discovermagazine.com/cosmicvariance/2008/12/29/...

d4rkph1b3r 11y ago
>Feynman argued[2] that this shows we do not arise from a random fluctuation, because (even though we're conscious), when we look far away the universe looks highly organized. Oh that is an interesting and compelling argument I have not heard! Thank you for sharing.
- effie 11y ago
  Both Boltzmann's idea of fluctuation and Feynman's argument against it are unfortunately devoid of meaning, because we do not know how highly organized and thermal death universe look like. We never saw and probably never will see another state of the universe and there is no way to experiment with it.
  - d4rkph1b3r 11y ago
    His argument is sound. If there is infinite #s of universes, or the universe keeps reforming infinitely (implication being it will have varying degrees of uniformity), then it's mathematically probable that we would be boltzman brain's in a less coherent universe. We don't observe that.

ylem 11y ago

For those interested in the anthropomorphic principle, this paper by Wald might be interesting: http://arxiv.org/pdf/gr-qc/0507094v1.pdf http://arxiv.org/pdf/gr-qc/0507094v1.pdf

trhway 11y ago

>The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Why did the universe not start out in a state that is essentially equal to the heat-death [1]? taken as a closed system, our Universe's initial state was a heat-death and it would stay here, nothing would happen. Fortunately or unfortunately our Universe is embedded into previous very old and cool Universe, and this gradient is what drives the expansion of our Universe and thus provides for all the things we see happening to happen, including life (which is just entropy maximizing process in some conditions). 100-200+B year later our Universe will too be very cool and expanded very "thin". The matter will be collected into several hyper-super-black holes with Schwarzschild radii of tens or even hundreds o billions of light years - some probably bigger than our visible Universe (which has 10B light years Schwartzild radius). The matter inside a regular black hole is neutrons being driven into higher and higher states as result of mass being added into the black hole. At some point the neutrons get to split into gluons/quarks and those would continue to be driven into more energetic states as more mass is added, and may be split as a result into something else too. At the same time the space around becomes "thinner" and cooler. At some point, when even more mass is added, and thus this "soup" becomes even more energetic, beyond currently known physics unfortunately, something happens to the gravitational force what has been keeping it together and it explodes and start expanding (as there is extremely high gradient between the "soup" and the space of the old Universe - thus that will be a birth of new Universe inside our old Universe, inside the parent Universe of our Universe ... ad infinitum ... with non-zero gradient, though smaller and smaller as parent-child Universe pair is getting older...

effie 11y ago

> Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible. Entropy does not always increase in time, because entropy is rarely a function of time. The most common meaning of the word is a thermodynamic quantity that is not, in general, defined in non-equilibrium states. It is a function of state variables rather than time. What people are talking about when they say "entropy increases in time" is actually some variant of minus Boltzmann H-function. This kind of resembles thermodynamic entropy, but is a distinct and less general concept. There are processes where entropy gets higher but "entropy" (minus Boltzmann H-function) get lower. If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. It is not even clear how to define entropy of the system in between, since it is in highly non-equilibrium state.

trhway 11y ago
>If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. Moving an object to higher gravitational potential decreases the entropy of the system (and thus requires work, unsurprisingly). Mixing oil into water means you displace some volume of water which were closer to Earth with oil bubbles (which are lighter than equivalent volume of water) while you force the displaced water volume higher/further from Earth. Thus by mixing lighter oil with heavier water you decrease the entropy of the gravitational system consisting of the oil, water and Earth. Left to its own devices, the system evolves along the entropy increasing gradient - heavy water goes down displacing lighter oil up, thus decreasing the gravitational potential of the system (the friction during that "unmixing" is the work of the gravitational force that ultimately results in the heat that is lost away into the environment).
- effie 11y ago
  When the fluids are mixed by a spoon, surely work has been done by the stirring spoon on the system and energy of the system increased. But this does not by itself imply entropy of the system increased. The reason is the system got to a non-equilibrium state which has no macroscopic thermodynamic description and no unique way to assign entropy and detect its changes.

e12e 11y ago

bcbrown 11y ago

> The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Here's a possibility: if you "start" at a random state, after enough exploration of the state space, there would be a local minima that was arbitrarily well-ordered. Both directions of time would then view that as the "past", and the other direction as "future". These perceptions as to the arrow of time would last until a state equivalent to heat death is reached, at which point the "arrow" of time would flip around again.